MASTER AND PUPIL
has done something everlasting! His ideas will always exercise a
fertilizing influence on our science.'
The same might be said for Weierstrass, and the creative
ideas with which he fertilized mathematics were for the most
part thought out while he was an obscure schoolteacher in
dismal villages where advanced books were unobtainable, and
at a time of economic stress when the postage on a letter
absorbed a prohibitive part of the teacher's meagre weekly
wage. Being unable to afford postage, Weierstrass was barred
from scientific correspondence. Perhaps it is as well that he was:
his originality developed unhampered by the fashionable ideas
of the time. The independence of outlook thus acquired charac-
terized his work in later years. In his lectures he aimed to
develop everything from the ground up in his own way and
made almost no reference to the work of others. This occasion-
ally mystified his auditors as to what was the master's and
what another's.
It will be of interest to mathematical readers to note one or
two stages in Weierstrass' scientific career. After his proba-
tionary year as a teacher at the Gymnasium at Miinster,
Weierstrass wrote a memoir on analytic functions in which,
among other things, he arrived independently at Cauehy's
integral theorem - the so-called fundamental theorem of
analysis. In 1842 he heard of Cauchy's work but claimed no
priority (as a matter of fact Gauss had anticipated them both
away back in 1811, but as usual had laid his work aside to
ripen). In 1842, at the age of twenty-seven, Weierstrass applied
the methods he had developed to systems of differential equa-
tions - such as those occurring in the Newtonian problem of
three bodies, for example; the treatment was mature and
rigorous. These works were undertaken without thought of
publication merely to prepare the ground on which Weierstrass1
lifework (on Abelian functions) was to be built.
In 1842 Weierstrass was assistant teacher of mathematics
and physics at the Pro-Gymnasium in Deutsch-Krone, West
Prussia, Presently he was promoted to the dignity of ordinary
teacher. In addition to the subjects mentioned the leading
analyst in Europe also taught German, geography, and writing
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